Several national governments, including the United States (U.S.) of America, are presently developing a terrestrial position determination system, referred to generically as a global positioning system (GPS). A GPS is a satellite-based radio-navigation system which is intended to provide highly accurate three-dimensional position information to receivers at or near the surface of the Earth.
The U.S. government has designated its GPS the "NAVSTAR." The NAVSTAR GPS is expected to be declared fully operational by the U.S. government in 1993. The government of the former Union of Soviet Socialist Republics (U.S.S.R.) is engaged in the development of a GPS known as "GLONASS". Further, two European systems known as "NAVSAT" and "GRANAS" are also under development. For ease of discussion, the following disclosure focuses specifically on the NAVSTAR GPS. The invention, however, has equal applicability to other global positioning systems.
In the NAVSTAR GPS, it is envisioned that four orbiting GPS satellites will exist in each of six separate circular orbits to yield a total of twenty-four GPS satellites. Of these, twenty-one will be operational and three will serve as spares. The satellite orbits will be neither polar nor equatorial but will lie in mutually orthogonal inclined planes.
Each GPS satellite will orbit the Earth approximately once every 12 hours. This coupled with the fact that the Earth rotates on its axis once every twenty-four hours causes each satellite to complete exactly two orbits while the Earth turns one revolution.
The position of each satellite at any given time will be precisely known and will be continuously transmitted to the Earth. This position information, which indicates the position of the satellite in space with respect to time (GPS time), is known as ephemeris data.
In addition to the ephemeris data, the navigation signal transmitted by each satellite includes a precise time at which the signal was transmitted. The distance or range from a receiver to each satellite may be determined using this time of transmission which is included in each navigation signal. By noting the time at which the signal was received at the receiver, a propagation time delay can be calculated. This time delay when multiplied by the speed of propagation of the signal will yield a "pseudorange" from the transmitting satellite to the receiver.
The range is called a "pseudorange" because the receiver clock may not be precisely synchronized to GPS time and because propagation through the atmosphere introduces delays into the navigation signal propagation times. These result, respectively, in a clock bias (error) and an atmospheric bias (error). Clock biases may be as large as several milliseconds.
Using these two pieces of information (the ephemeris data and the pseudorange) from at least three satellites, the position of a receiver with respect to the center of the Earth can be determined using passive triangulation techniques.
Triangulation involves three steps. First, the position of at least three satellites in "view" of the receiver must be determined. Second, the distance from the receiver to each satellite must be determined. Finally, the information from the first two steps is used to geometrically determine the position of the receiver with respect to the center of the Earth.
Triangulation, using at least three of the orbiting GPS satellites, allows the absolute terrestrial position (longitude, latitude, and altitude with respect to the Earth's center) of any Earth receiver to be computed via simple geometric theory. The accuracy of the position estimate depends in part on the number of orbiting GPS satellites that are sampled. Using more GPS satellites in the computation can increase the accuracy of the terrestrial position estimate.
Conventionally, four GPS satellites are sampled to determine each terrestrial position estimate. Three of the satellites are used for triangulation, and a fourth is added to correct for the clock bias described above. If the receiver's clock were precisely synchronized with that of the GPS satellites, then this fourth satellite would not be necessary. However, precise (e.g., atomic) clocks are expensive and are, therefore, not suitable for all applications.
For a more detailed discussion on the NAVSTAR GPS, see Parkinson, Bradford W. and Gilbert, Stephen W., "NAVSTAR: Global Positioning System--Ten Years Later," Proceedings of the IEEE, Vol. 71, No. 10, October 1983; and GPS: A Guide to the Next Utility, published by Trimble Navigation Ltd., Sunnyvale, Calif., 1989, pp. 1-47, both of which are incorporated herein by reference. For a detailed discussion of a vehicle positioning/navigation system which uses the NAVSTAR GPS, see commonly owned U.S. pat. appl. Ser. No. 07/628,560, entitled "Vehicle Position Determination System and Method," filed Dec. 3, 1990, which is incorporated herein by reference.
In the NAVSTAR GPS, the electromagnetic signals from each satellite are continuously transmitted using a single carrier frequency. Each satellite, however, uses a different modulation gold code to allow differentiation of the signals. The carrier frequency is modulated using a pseudorandom signal which is unique to each GPS satellite. Consequently, the orbiting GPS satellites can be identified when the navigation signals are demodulated.
Furthermore, the NAVSTAR GPS envisions two modes of modulation for the carrier wave using pseudorandom signals. In the first mode, the carrier is modulated by a "C/A signal" and is referred to as the "Coarse/Acquisition mode". The Coarse/Acquisition or C/A mode is also known as the "Standard Positioning Service". The C/A signal is a gold code sequence having a chip rate of 1.023 MHz. Gold code sequences are known in the art.
A chip is one individual pulse of the pseudorandom code. The chip rate of a pseudorandom code sequence is the rate at which the chips in the sequence are generated. Consequently, the chip rate is equal to the code repetition rate divided by the number of members in the code. With respect to the C/A mode of the NAVSTAR GPS, there exists 1,023 chips in each gold code sequence and the sequence is repeated once every millisecond. Use of the 1.023 MHz gold code sequence from four orbiting GPS satellites enables the terrestrial position of an Earth receiver to be determined to an approximate accuracy of within 60 to 100 meters (with 95% confidence).
The second mode of modulation in the NAVSTAR GPS is commonly referred to as the "precise" or "protected" (P) mode. In the P-mode, the pseudorandom code has a chip rate of 10.23 MHz. Moreover, the P-mode sequences are extremely long, so that the sequences repeat no more than once every 267 days. As a result, the terrestrial position of any Earth receiver can be determined to within an approximate accuracy of 16 meters (spherical error probable). The P-mode is also known as the "Precise Positioning Service".
The P-mode sequences are held in secrecy by the United States government and are not made publicly available. The P-mode is intended for use only by Earth receivers specifically authorized by the United States government. Thus, the P-mode modulated data is generally not available so that many GPS users must rely solely on the GPS data provided via the C/A mode of modulation. This relegates most users to a less accurate positioning system.
The clock and atmospheric errors discussed above add to the inaccuracy of the positioning system. Other errors which affect GPS position computations include receiver noise, signal reflections, shading, and satellite path shifting (e.g., satellite wobble). These errors result in computation of incorrect pseudoranges and incorrect satellite positions. Incorrect pseudoranges and incorrect satellite positions, in turn, lead to a reduction in the precision of the position estimates computed by a vehicle positioning system.
Methods are available for compensating or correcting for many of these errors. However, atmospheric errors and satellite path shifting have non-linear components. These errors account for a .+-.2 meter limitation on positioning precision.
A conventional method which attempts to compensate for these non-linear errors uses a differential system (discussed below) to produce a linear bias for each pseudorange (i.e., a bias is calculated for each satellite). A base station, having a fixed, known position, computes a pseudorange to each satellite. The base station further computes a distance between its known position and the position of each satellite (computed from the ephemeris data). By comparing the pseudorange to each computed distance, a pseudorange bias can be computed for each satellite. The pseudorange bias for each satellite can then be transmitted to the vehicle for use in the position estimate computations.
This method, however, does not account for the non-linear nature of the errors. For example, if ephemeris data indicates that a satellite is at a position P.sub.1 and the satellite is actually at a position P.sub.2 (e.g., due to wobble), then a single linear bias which modifies the pseudorange cannot completely correct for the wobble.
Accordingly, what is needed is a method to correct for these non-linear errors so that the precision of vehicle position estimates may be improved.